Question

According to the Investment Company Institute, 40% of U.S. households have an Individual Retirement Account (IRA). Assuming the population proportion to be π = 0.40 and that a simple random sample of 400 households has been selected:
a. What is the expected value of p = the proportion in the sample having an IRA?
b. What is the standard error of the sampling distribution of the proportion?
c. What is the probability that at least 35% of those in the sample will have an IRA?
d. What is the probability that between 38% and 45% of those in the sample will have an IRA?